In a quadrature mixer arrangement, one or more input signals is typically mixed with two versions of a translation frequency signal to translate the input signals by the translation frequency (often denoted local oscillator—LO—frequency) to produce one or more output signals. The two versions of the translation frequency signal are typically an in-phase version and a quadrature-phase version having a mutual phase difference of π/2 or close thereto.
Quadrature mixers may, for example, be used in the form of harmonic rejection mixers. Good harmonic rejection may be important to achieve performance requirements, for example, in carrier aggregation receivers, television receivers, and software defined radio receivers.
Time and amplitude discrete implementations of harmonic rejection mixers have been described in, for example, WO2010/000603, L. Sundström, et al., “Harmonic rejection mixer at ADC input for complex IF dual carrier receiver architecture,” IEEE Radio Frequency Integrated Circuits Symposium, June 2012, and L. Sundström, et al., “Complex IF harmonic rejection mixer for non-contiguous dual carrier reception in 65 nm CMOS,” IEEE European Solid-State Circuits Conference, September 2012.
FIGS. 1A and 1B illustrate schematically an example complex intermediate frequency (IF) dual carrier receiver and a corresponding example implementation of a complex IF mixer, 100A, 100B.
In the example illustrated in FIG. 1A, a dual carrier signal 101 comprising two components 140, 141 is input to a low-noise amplifier (LNA) 102. The two components 140, 141 are located on opposite sides of a radio frequency (fRF).
The output 103, 104 of the LNA is mixed with a radio frequency cosine signal 105 in an in-phase mixer 107 and with a radio frequency sinus signal 106 in a quadrature-phase mixer 108. It should be noted that, throughout the disclosure, a reference to a cosine, sinus or sinusoidal signal or function comprises a simplified figurative description and that all functional equivalents are to be construed as embraced therein. For example, the cosine and sinus signals 105, 106 of FIG. 1A may, in an actual implementation, comprise hard-switched signals (representing staircase-type functions which approximate the cosine and sinus signals respectively).
The down-converted signals are filtered in respective low-pass filters (LPF) 109, 110 to exclude any higher frequency signal components, and the filtered signals 111, 112 comprise the two dual carrier components 142, 143, which are located at an intermediate frequency (fIF) on opposite sides of zero frequency. The filtered signal 111 is termed in-phase intermediate frequency signal IIF, and the filtered signal 112 is termed quadrature-phase intermediate frequency signal QIF.
The in-phase intermediate frequency signal and the quadrature-phase intermediate frequency signal are input to a complex IF mixer 100A comprising first and second intermediate frequency mixers (IF MIX) 113, 114. The first intermediate frequency mixer 113 is adapted to provide in-phase and quadrature-phase baseband components 127, 128 of the first dual carrier component 140, 142, 144 and the second intermediate frequency mixer 114 is adapted to provide in-phase and quadrature-phase baseband components 129, 130 of the second dual carrier component 141, 143, 145. The signals 127, 128, 129, 130 provided by the complex IF mixer 100A may be filtered and converted to the digital domain in respective low-pass filters (LPF) 115, 116, 117, 118 and analog-to-digital converters (ADC) 119, 120, 121, 122 to produce digital in-phase and quadrature-phase baseband signals of the first and second dual carrier component 123, 124, 125, 126.
In a typical example, the first intermediate frequency mixer 113 may implement a multiplication by exp(jωIFt), wherein the complex input signal 111 and 112 is translated to the complex output signal 127 and 128. Similarly, the second intermediate frequency mixer 114 may implement a multiplication by exp(−jωIFt), wherein the complex input signal 111 and 112 is translated to the complex output signal 129 and 130.
FIG. 1B illustrates one example of a practical implementation of a complex IF mixer 100B which may, for example, be used as the complex IF mixer 100A of FIG. 1A. The example complex mixer 100B has a complex input signal 111b, 112b and two complex output signals 127b, 128b and 129b, 130b. 
The first in-phase output signal 127b is produced by mixing the in-phase input signal 111b with an intermediate frequency cosine signal in an in-phase mixer 151 and subtracting the quadrature-phase input signal 112b mixed with an intermediate frequency sinus signal in a quadrature-phase mixer 152 there from. The first quadrature-phase output signal 128b is produced by mixing the quadrature-phase input signal 112b with an intermediate frequency cosine signal in a quadrature-phase mixer 154 and adding the in-phase input signal 111b mixed with an intermediate frequency sinus signal in a quadrature-phase mixer 153 thereto.
The second in-phase output signal 129b is produced by mixing the in-phase input signal 111b with an intermediate frequency cosine signal in the in-phase mixer 151 and adding the quadrature-phase input signal 112b mixed with an intermediate frequency sinus signal in the quadrature-phase mixer 152 thereto. The second quadrature-phase output signal 130b is produced by mixing the quadrature-phase input signal 112b with an intermediate frequency cosine signal in the quadrature-phase mixer 154 and subtracting the in-phase input signal 111b mixed with an intermediate frequency sinus signal in the quadrature-phase mixer 153 there from.
It should be noted that the multiplications by exp(jωIFt) and exp(−jωIFt) may be interchanged and the multiplications by cos(ωIFt) and sin(ωIFt) may be replaced by multiplications by cos(ωIFt) and −sin(ωIFt). Other variations are also possible as is well known in the art.
In some quadrature mixer arrangements, the translation frequency signal versions (e.g. the intermediate frequency sinus and cosine signals of FIG. 1B) may be time-discrete (and possibly amplitude-discrete, i.e. quantized) representations of the sinusoid signals with appropriate phase shift. Thus, the translation frequency signal versions correspond to a sampled (and possibly quantized) sinusoid signal. The number of samples per translation frequency signal period is termed the over-sampling rate (OSR) herein. For reasons of spectral purity and low complexity, mixers may operate with an integer number of samples per translation frequency signal period (or, equivalently, LO period). Thus, the over-sampling rate is an integer in such implementations.
In the scenario with time-discrete translation frequency signals, there is no explicit LO waveform provided to each mixer in the time-discrete mixer implementation. Rather, the mixer arrangement is driven by a clock with a rate that equals the over-sampling rate times the translation frequency and each mixer can be said to have an equivalent LO waveform. Regardless of how the mixer arrangement is implemented, there will always be either an explicit LO waveform or an equivalent (implicit) LO waveform associated with each mixer. Any reference herein to LO waveform (or related parameters or signals) is meant to embrace both the explicit and implicit scenario.
As mentioned above, a quadrature mixer typically consists of mixer elements operated with a phase difference of π/2 (90 degrees). If these mixer elements are to be operated in an identical fashion (generating identical equivalent LO waveforms with a phase difference of π/2) in a time-discrete and quantized scenario, the over-sampling rate should be a multiple of 4 so that the time-discrete translation frequency signal sequences are shifted versions of each other (the shift corresponding to a time shift). In a typical implementation this means that the rate of the clock driving the mixer and/or the translation frequency signal generator should be 4 times N times the translation frequency, where N is an integer. Due to practical reasons (e.g., limited frequency range of the clock) the over-sampling rate is often limited to, for example, an integer between 6 and 20, leaving only the alternatives {8,12,16,20} given the restriction explained above. In some scenarios, the time-discrete translation frequency signal sequences may be chosen such that they are not (time) shifted versions of each other and still provide a high harmonic rejection.
Regardless of the time-discrete translation frequency signal sequences being different or not, a requirement to provide high harmonic rejection while the over-sampling rate is not a multiple of 4 will generally lead to that the magnitude and phase of the fundamental frequency component of one sequence will be different from that of the other sequence. This translates to a severely limited image rejection ratio.
Therefore, there is a need for quadrature mixer arrangements where an arbitrary over-sampling rate may be applied, preferably while maintaining a high image rejection ratio.